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It is not like we are going to be able to store one bit per molecule of water (or even per 10,000 molecules) in a full liter anytime soon. If it was possible at a relatively low energetic cost, it would equal to a Maxwell demon and "refute" thermodynamics
If by refuting thermodynamics you mean refuting the second law of thermodynamics, let's assume that storing information in water molecules takes 'x' [ Joule / bit ] energy. What is the relatively low value of 'x' which already violates the second law of thermodynamics and how does this violation happen? Why is not the second law of thermodynamics violated if 'x' has a higher value than that?
It seems that I have to answer my own question.
I have looked into this and I have found out that the minimum energy required to store one bit of information is determined by Landauer's principle ( http://en.wikipedia.org/wiki/Landauer's_principle ) and at room temperature it is:
2.85 Zeptojoule ( 2.85*10^-21 Joule )
The solar energy absorbed by Earth per year is ( http://en.wikipedia.org/wiki/Solar_energy ):
3850000 Exajoule ( 3.85*10^24 Joule )
This means that using all solar energy absorbed by Earth the rate at which you can store information is 3.85*10^24/2.85*10^-21 [ bit / year ] which is:
1.35*10^45 [ bit / year ]
This is on the order of legal chess positions.
Chess can not be solved as the combinations of moves and positions equal a number near infinite.
It is a borderline case as far as a strong solution is concerned, but you can't say for certain that it is impossible because it breaches no theoretical limit. Within theoretical limits there is always room for creativity.
We cannot say with 100% certainty that chess will never be solved but a very good guess is that it will never be solved before our sun explodes.
We cannot say with 100% certainty that chess is a draw when both sides make no errors but the best chess players [GMs and above] are very sure [99.9% sure] that chess is a draw when both sides play without errors.
I am 99.9% sure that there have been thousands of games played already with both sides making no errors. [error meaning a mistake which would change the outcome of the game if the other side player/computer played perfectly]
It is certain that chess can be solved in the weak sense practically and it is very likely that this will happen.
However the weak solution is not of too much interest ( it is almost certain that the starting position is a draw ). Only a strong solution can answer interesting questions about the merits of certain openings and endgames.
If it turns out for example that the king's gambit accepted is a win for black: now, this would be a non trivial result.
I'm also interested in questions like whether white can make a move on the first move which loses ( does 1. f3 lose by force for example ).
Put a disk like object into space that orbits the Sun with the same period as Earth and always shows one face towards the Sun and the other face towards outer space. The temperature of outer space is that of the cosmic microwave radiation: 2.7 K ( http://en.wikipedia.org/wiki/Outer_space ). Use this side to store information. This can be done two orders of magnitude more efficiently than on Earth because Landauer's limit depends on the temperature. Use the other side towards then Sun to collect the energy needed for storage.
Filter out illegal positions and account for basic symmetries. At least 3 orders of magnitude.
You are already have improved 5 orders of magnitude.
If on Earth it takes a year to store bits on the order of the upper bound of the number of legal chess positions, then if you improve upon this by 5 orders of magnitude and store them on a space device described above, the radius of the device should be ( http://www.wolframalpha.com/input/?i=sqrt%28%28area+of+Earth%29%2F%282*10%5E5*pi%29%29 ):
It can be organized that the device is not too far away from Earth all year, so the speed of communication with the device is not limited by the light barrier in any significant way.
Is it not possible to built a 28 km radius space device? It is hard, but is it impossible?
There are more Important things in Life than Solving Chess! like how to make Perfect Beer!
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